Evolution as an Algorithm

For some yes, and others, no.
Even if you could replicate data for the many variables (don't forget environment) over a time period and predict a new species that actually exists, you would run into the following argument:
1. That is one explanation, but not the only possibility.
2. Another possibility, as written in __religious document__ is that God/Allah/etc. created it.The algorithm approach is similar to what I would call a pattern. I see a pattern of change in all aspects of life, not just biology (that's why I picked "ThingsChange"). For example, the pattern applies to business, culture, and religion, too. Hence, that gives me sufficient confidence without having to write a computer program (which uses languages that have evolved).

In the classic definition, you are correct, but that is getting muddy these days, especially with machines receiving input from sensors and even other independent devices. The military has some very sophisticated networked devices and sensors that each have algorithms that determine the reaction to interactive input from many concurrent sources.
My point is that there can still be a high-level algorithm governing many small ones, and this concept fits the biological model, too.